I think it's ok for them to have stocks, they just should be put into a blind trust to manage, and they shouldn't be able to make any transactions outside of that for the duration of their term in office.
Hmm, should there be limits? I agree in principle that receiving public money as income should probably make your income records public knowledge, but... do we need to expose the personal finances of every park ranger? every military member? NASA engineers? Education board members? Or limit it specifically to elected positions? Would it then only apply to elected judges but not appointed ones? Every level - fed, state, county, city?
The problem is, your tax records have enough information on them to expose you to identity theft. High-profile positions like the President will have enough people watching all their records to prevent any serious identity theft attempts, but setting up that kind of oversight for every public official would be incredibly difficult and expensive. Exposing some government positions to identity theft like this creates some pretty serious security concerns. Just exposing the address of a judge could put them at risk.
Government employees way too often forget they are public servants. The public has a right to know their salaries, to record them while they are working, and to expect respect and transparency.